DO the hotels in South Africa have hair dryers? DO I need a converter?

Any decent lodging around the world has hair dryers. Trying to bring one from a 110v country can be fraught so don't bother. You can buy one that's dual voltage and in the dark ages when I used a dryer I had one that worked. But many here will report otherwise. I suggest you email the places you'll stay to confirm they have them. The alternative is to do as many of us do, go natural or short.